Dbms_ouptut.put_line is a quick and dirty way to get output for debugging. If you're using it for any other purpose, change now, and the problem will become merely an acadeic question.

LINESIZE might cause an output line to wrap, or to get truncated, but it won't cause a line to disappear. If your LINESIZE is too short (than is, if you have lines with more than 3500 characters), then you might get more output lines than you expected, not fewer. If LINESIZE is longer than it needs to be, it won't change the output one way or another.

There's nothing special about the character '/' in dbms_output. '/' isn't causing the problem any more than 'B' or ',' or space.